https://doi.org/10.48550/arXiv.2312.12623

Summary

  • Non-blazar AGN PKS 0521-36 observed over 15 years by Fermi-LAT telescope.
  • Lomb-Scargle and wavelet analysis reveals three Quasi-periodic oscillations (QPOs).
  • GP modelling revealed two more QPOs.
  • First long-term QPO detected from a non-blazar AGN.
  • Cause of QPOs remains unclear.
  • Evidence for QPOs seems inconsistent.

Data

  • ROI is circular region of 10\(^\circ\) radius centred at PKS 0521-36
  • 15 years of observations by Fermi-LAT (August 2008 - 2023)
    • MJD 54683 – MJD 60187 (5,504 days)
  • \(\gamma\)-ray light curve (0.1 – 300 GeV)
  • Uniformly sampled

Method

  1. Compute Lomb-Scargle periodogram.
  2. Compute Weighted wavelet Z-transform.
  3. Fit Gaussian Process model with different kernels:
    • Damped Random Walk,
    • Simple Harmonic Oscillator, and
    • combinations thereof.
  4. Choose best kernel combination using BIC.
  5. Look for “significant” peaks in power.

“Significance” estimation

  • Nice application of bootstrapping to get the distribution of light curves.
  • Not clear how \(\beta = 0.48 \pm 0.16\) is determined.

Results: LSP and WWZ

T = 268, 295, 806 days.

Results: GP Model

Results: GP PSD

Statistical Comments

  • CARMA is a stochastic process
    • CAR(1) is a special case that can be expressed as GP.
  • Computationally heavy, N \(\approx\) 500, 32 chains, 15000 steps.
  • No mention of priors.
  • Where does the “quasi” come from?
    • LSP and WWZ target periodicity, not quasi-periodicity.
    • Why not use QP GP kernels.
  • [Aside] More data \(\rightarrow\) more likely to reach significance.
    • 3\(\sigma\) vs. 5\(\sigma\) might not itself be significant.

Note on BIC

\[\textrm{BIC} = -2\mathcal{L} + K \log N\]

  • BIC should only be used to compare between models that are subsets of eachother.
  • Not surprising that BIC increases with model complexity.

Manuscript queries

  • QPOs don’t match between LSP/WWZ and GP models
    • \(T = 268, 295, 806\) days vs. \(T = 283, 886\) days.
    • Used different date ranges MJD 54683 – 60187 (15y) vs. MJD 55358 – 59547 (11.4y) for each.
  • Kelly et al. (2009) and Li & Wang (2018) are analyses of optical not \(\gamma\)-ray light curves.
  • Insufficient information to reproduce, e.g., source code.

QPO vs BH Mass